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To find the separation between the two negatively charged dielectric balls, we can use Coulomb’s law, which describes the electrostatic force between two point charges.
1. Given:
– Charge of each ball, ( q = 1 , mu C = 1 times 10^{-6} , C )
– Mass of each ball, ( m = 10 , g = 0.01 , kg )
– The equation for the electrostatic force between two charges is given by:
[
F = k frac{|q_1 q_2|}{r^2}
]
where ( F ) is the electrostatic force, ( k ) is Coulomb’s constant (approximately ( 8.99 times 10^9 , N m^2/C^2 )), ( r ) is the separation between the charges, and ( q_1 ) and ( q_2 ) are the charges of the two balls.
2. For this configuration:
– Since one ball is restrained, the force acting on the upper ball must balance the gravitational force acting on it.
3. Calculating the gravitational force ( F_g ) acting on the upper ball:
[
F_g = m g
]
where ( g ) (acceleration due to gravity) is approximately ( 9.81 ,